How can I simulate powder with a particle system?
Particles:

You could use Newtonian or Fluid type Particles to simulate the powder, with the gears and funnel as Collision objects.

For example:


Add a plane (ShiftA> Mesh > Plane) and add a particle system to it.
Set the Lifetime to a number greater than the scene End frame
Set the Physics to Fluid in Particles > Physics
Add an Icosphere (ShiftA> Mesh > Icosphere). You may want to set the Subdivisions to 1 in the Redo panel or the F6 menu for situations with many small particles.
Set the particle Dupli Object to the icosphere in Particles > Render > Dupli Object
Set the size in Physics as desired, I used .001
Enable Simple in Particles > Children and set the Radius and Uniform Roughness as desired. 


The Radius defines how far child particles are allowed from the real particle
Uniform roughness gives some randomness to the locations of child particles

Set the Cache Step in Particles > Cache to 1, this will record the location of each particle every frame. The default of 10 often gives strange results.
For object you want to collide with the powder:


Add a Collision physics modifier in Properties > Physics
Increase the Particle Damping factor. By default particles will bounce very high, this setting controls how much velocity the particle loses on collision with this object.

Bake